报告题目：Generalised bi-Hamiltonian structures and bi-flat F-manifolds 

报告人：Zhe Wang，日本理化学研究所(RIKEN) 

报告时间：4月23日 10:00-11:00

报告地点：二教2302

摘要：

Hamiltonian structures and bi-Hamiltonian structures of hydrodynamic type are fundamental in the theory of integrable hierarchies. They are closely related to the geometry of Frobenius manifolds and play important roles in the study of higher genus part of cohomological field theories. However, there are many integrable hierarchies arising from the geometry of moduli space of stable curves which do not admit Hamiltonian structures in the usual sense. In this talk, we introduce the notion of generalised (bi-)Hamiltonian structures of hydrodynamic type, which are more flexible than the usual ones and can be naturally associated to (bi-)flat F-manifolds. We show that the principal hierarchies associated to (bi-)flat F-manifolds are generalised (bi-)Hamiltonian systems with respect to these structures. This provides a new perspective on the integrable hierarchies arising from F-manifolds and opens up new directions for their study. This talk is based on a joint work with Paolo Lorenzoni.